while anyone can put arrows in their hands, the arrows do not act as weapons for anyone at all.
i.e. equip 2 arrows and try to hit something, you'll never land a hit because they're not weapons. you can't even attempt to hit.
See below for an example on one of my chars. 2 dirty rag arrows, you can see with the attack button nothing happens related to an attack.
https://prnt.sc/jtn95l
https://prnt.sc/jtnbbo
on my character Coal Chamber, I have both the Friar's Staff and the Theurg Staff (some say a waste, I say science). I again have dirty rag arrows, but as you can see that an attempt was made to attack with the setup being theurg+arrows
https://prnt.sc/jtnaqr
https://prnt.sc/jtnbgh
So yes any char can equip arrows, but they aren't weapons and can't attack. So my question is again, having both staffs now does the ability to equip 2 arrows and ATTACK with them mean that the arrow=weapon for monks trait a passive trait for the Friar's staff that is always active regardless of class?